Turbine nozzle profile

ABSTRACT

Various embodiments of the invention include turbine nozzles and systems employing such nozzles. Various particular embodiments include a turbine nozzle having: an airfoil having: a suction side; a pressure side opposing the suction side; a leading edge spanning between the pressure side and the suction side; and a trailing edge opposing the leading edge and spanning between the pressure side and the suction side; and at least one endwall connected with the airfoil along the suction side, pressure side, trailing edge and the leading edge, the at least one endwall including an axisymmetric contour.

FIELD OF THE INVENTION

The subject matter disclosed herein relates to turbomachines. More particularly, the subject matter disclosed herein relates to components within turbomachines such as gas and/or steam turbines.

BACKGROUND OF THE INVENTION

Some aircraft and/or power plant systems, for example certain jet aircraft, nuclear, simple cycle and combined cycle power plant systems, employ turbines (also referred to as turbomachines) in their design and operation. Some of these turbines employ airfoils (e.g., turbine blades, blades, airfoils, etc.) which during operation are exposed to fluid flows. These airfoils are configured to aerodynamically interact with the fluid flows and generate energy (e.g., creating thrust, turning kinetic energy to mechanical energy, thermal energy to mechanical energy, etc.) from these fluid flows as part of power generation. As a result of this interaction and conversion, the aerodynamic characteristics and losses of these airfoils have an impact on system and turbine operation, performance, thrust, efficiency, and power.

BRIEF DESCRIPTION OF THE INVENTION

Various embodiments of the invention include turbine nozzles and systems employing such nozzles. Various particular embodiments include a turbine nozzle having: an airfoil having: a suction side; a pressure side opposing the suction side; a leading edge spanning between the pressure side and the suction side; and a trailing edge opposing the leading edge and spanning between the pressure side and the suction side; and at least one endwall connected with the airfoil along the suction side, pressure side, trailing edge and the leading edge, the at least one endwall including an axisymmetric contour.

A first aspect of the invention includes a turbine nozzle having: an airfoil having: a suction side; a pressure side opposing the suction side; a leading edge spanning between the pressure side and the suction side; and a trailing edge opposing the leading edge and spanning between the pressure side and the suction side; and at least one endwall connected with the airfoil along the suction side, pressure side, trailing edge and the leading edge, the at least one endwall including an axisymmetric contour.

A second aspect of the invention includes a static nozzle section having: a set of static nozzles, the set of static nozzles including at least one nozzle having: an airfoil having: a suction side; a pressure side opposing the suction side; a leading edge spanning between the pressure side and the suction side; and a trailing edge opposing the leading edge and spanning between the pressure side and the suction side; and at least one endwall connected with the airfoil along the suction side, pressure side, trailing edge and the leading edge, the at least one endwall including an axisymmetric contour, wherein at least one of the suction side or the pressure side of the airfoil includes a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in TABLE I, wherein the coordinate values are non-dimensional values of from 0 to 1 convertible to distances by multiplying the values by a leading edge height expressed in units of distance, and wherein X and Y values connected by smooth continuing arcs define airfoil profile sections at each distance Z along the airfoil, the profile sections at the Z distances being joined smoothly with one another to form the airfoil profile, wherein the Cartesian coordinate values have an origin at a root of the leading edge of the airfoil.

A third aspect of the invention includes a turbine nozzle having: an airfoil having: a suction side; a pressure side opposing the suction side; a leading edge spanning between the pressure side and the suction side; and a trailing edge opposing the leading edge and spanning between the pressure side and the suction side; and at least one endwall connected with the airfoil along the suction side, pressure side, trailing edge and the leading edge, wherein at least one of the suction side or the pressure side of the airfoil includes a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in TABLE I, wherein the coordinate values are non-dimensional values of from 0 to 1 convertible to distances by multiplying the values by a leading edge height expressed in units of distance, and wherein X and Y values connected by smooth continuing arcs define airfoil profile sections at each distance Z along the airfoil, the profile sections at the Z distances being joined smoothly with one another to form the airfoil profile, wherein the Cartesian coordinate values have an origin at a root of the leading edge of the airfoil.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other features of this invention will be more readily understood from the following detailed description of the various aspects of the invention taken in conjunction with the accompanying drawings that depict various embodiments of the invention, in which:

FIG. 1 shows a three-dimensional partial cut-away perspective view of a portion of a turbine according to an embodiment of the invention.

FIG. 2 shows a schematic three-dimensional depiction of a turbine nozzle including an airfoil and endwalls according to various embodiments of the invention.

FIG. 3 shows a comparison between a linear outer flow path and a curved axisymmetrical outer flow path contour according to various embodiments of the invention.

FIG. 4 shows a schematic three-dimensional depiction of a plurality of turbine nozzles according to various embodiments of the invention.

FIG. 5 shows a schematic block diagram illustrating portions of a multi-shaft combined cycle power plant system according to embodiments of the invention; and

FIG. 6 shows a schematic block diagram illustrating portions of a single-shaft combined cycle power plant system according to embodiments of the invention.

It is noted that the drawings of the invention are not necessarily to scale. The drawings are intended to depict only typical aspects of the invention, and therefore should not be considered as limiting the scope of the invention. It is understood that elements similarly numbered between the FIGURES may be substantially similar as described with reference to one another. Further, in embodiments shown and described with reference to FIGS. 1-6, like numbering may represent like elements. Redundant explanation of these elements has been omitted for clarity. Finally, it is understood that the components of FIGS. 1-6 and their accompanying descriptions may be applied to any embodiment described herein.

DETAILED DESCRIPTION OF THE INVENTION

As noted herein, various aspects of the invention are directed toward turbine nozzles. Particular aspects of the invention include turbine nozzles having at least one endwall with an axisymmetric contour.

In contrast to conventional turbine nozzles, aspects of the invention include a turbine nozzle (e.g., a static nozzle for directing a working fluid such as gas or steam) having an axisymmetric contour. This axisymmetric contour can provide for enhanced performance, efficiency and/or durability of the nozzle (and associated turbine stages and turbine machines) when compared with conventional nozzles.

As used herein, the terms “axial” and/or “axially” refer to the relative position/direction of objects along axis A, which is substantially parallel to the axis of rotation of the turbomachine (in particular, the rotor section). As further used herein, the terms “radial” and/or “radially” refer to the relative position/direction of objects along axis (r), which is substantially perpendicular with axis A and intersects axis A at only one location. Additionally, the terms “circumferential” and/or “circumferentially” refer to the relative position/direction of objects along a circumference which surrounds axis A but does not intersect the axis A at any location. Further, the terms leading edge/pressure side refer to components and/or surfaces which are oriented upstream relative to the fluid flow of the system, and the terms trailing edge/suction side refer to components and/or surfaces which are oriented downstream relative to the fluid flow of the system.

In the following description, reference is made to the accompanying drawings that form a part thereof, and in which is shown by way of illustration specific embodiments in which the present teachings may be practiced. These embodiments are described in sufficient detail to enable those skilled in the art to practice the present teachings and it is to be understood that other embodiments may be utilized and that changes may be made without departing from the scope of the present teachings. The following description is, therefore, merely exemplary.

Referring to the drawings, FIG. 1 shows a perspective partial cut-away illustration of a turbine 10 (e.g., gas or steam turbine and/or aviation jet engine) according to various embodiments of the invention. Turbine 10 includes a rotor 12 that includes a rotating shaft 14 and a plurality of axially spaced rotor wheels 18. A plurality of rotating buckets 20 are mechanically coupled to each rotor wheel 18. More specifically, buckets 20 are arranged in rows that extend circumferentially around each rotor wheel 18. A static nozzle section 21 is shown including a plurality of stationary nozzles 22 circumferentially around shaft 14, and nozzles 22 are axially positioned between adjacent rows of buckets 20. Stationary nozzles 22 cooperate with buckets 20 to form a stage of turbine 10, and to define a portion of a flow path through turbine 10. As shown, static nozzle section 21 at least partially surrounds rotor 12 (shown in this cut-away view). It is understood that turbine 10 shown is a dual-flow turbine 10 that includes an axially centered inlet mouth which feeds two sets of turbine stages. It is understood that various teachings can be applied to axial turbines, e.g., axial inlet gas turbines that inlet a combustion gas from a first axial end and outlet that combustion gas to a second axial end after the gas has performed mechanical work on the turbine.

Returning to FIG. 1, in operation, gas 24 enters an inlet 26 of turbine 10 and is channeled through stationary nozzles 22. Nozzles 22 direct gas 24 against blades 20. Gas 24 passes through the remaining stages imparting a force on buckets 20 causing shaft 14 to rotate. At least one end of turbine 10 may extend axially away from rotating shaft 12 and may be attached to a load or machinery (not shown) such as, but not limited to, a generator, and/or another turbine.

In one embodiment, turbine 10 may include five stages. The five stages are referred to as L0, L1, L2, L3 and L4. Stage L4 is the first stage and is the smallest (in a radial direction) of the five stages. Stage L3 is the second stage and is the next stage in an axial direction. Stage L2 is the third stage and is shown in the middle of the five stages. Stage L1 is the fourth and next-to-last stage. Stage L0 is the last stage and is the largest (in a radial direction). It is to be understood that five stages are shown as one example only, and each turbine may have more or less than five stages. Also, as will be described herein, the teachings of the invention do not require a multiple stage turbine. In another embodiment, turbine 10 may comprise an aircraft engine used to produce thrust.

Turning to FIG. 2, a schematic three-dimensional depiction of a turbine nozzle (or simply, nozzle) 200 is shown according to various embodiments. Nozzle 200 is a stationary nozzle which forms an annulus of stationary nozzles in a stage of a turbine (e.g., turbine 10). That is, during operation of a turbine (e.g., turbine 10), nozzle 200 will remain stationary in order to direct the flow of working fluid (e.g., gas or steam) to one or more movable buckets (e.g., buckets 20), causing those movable buckets to initiate rotation of a rotor shaft (e.g., shaft 14). It is understood that nozzle 200 is configured to couple (mechanically couple via fasteners, welds, slot/grooves, etc.) with a plurality of similar or distinct nozzles (e.g., nozzles 200 or other nozzles) to form an annulus of nozzles in a stage of the turbine.

Returning to FIG. 2, turbine nozzle 200 can include an airfoil 202 having a suction side 204, and a pressure side 206 (obstructed in this view) opposing the suction side 204. Nozzle 200 can also include a leading edge 208 spanning between the pressure side 206 and the suction side 204, and a trailing edge 210 opposing leading edge 208 and spanning between pressure side 206 and suction side 204.

As shown, nozzle 200 can also include at least one endwall 212 (two shown) connected with airfoil 202. Endwall 212 can be connected with airfoil 202 along suction side 204, pressure side 206, trailing edge 210 and leading edge 208. In various embodiments, nozzle includes a fillet 214 connecting nozzle 200 and each endwall 212. Fillet 214 can include a weld or braze fillet, which may be formed via conventional MIG welding, TIG welding, brazing, etc.

As described herein, and in contrast to conventional turbine nozzles, turbine nozzle 200 can include at least one endwall 212 with an axisymmetric contour 218. That is, nozzle 200 includes an endwall 212 with a contour 218 proximate junction 220 between endwall 212 and suction side 204 of airfoil 202 that improves the flow area around airfoil 202 when compared with conventional nozzles.

In various embodiments, contour 218 allows for more efficient fluid flow across airfoil 202 than conventional nozzles 200, allowing for fewer heat load-related failures, and improving the efficiency of fluid flow within a turbine utilizing such a nozzle 200.

With reference to FIG. 1, in various embodiments, the nozzle 200 can include a first stage nozzle (L4), second stage nozzle (L3), third stage nozzle (L2), fourth stage nozzle (L1), or fifth stage nozzle (L0). In particular embodiments, nozzle 200 is a fourth stage nozzle (L1), and the improved flow profile across airfoil 200 and endwall 212 interface allows that fourth stage nozzle (L1) to withstand high-temperature gas at that fourth stage. In various embodiments, turbine 10 can include a set of nozzles 200 in only the fourth stage (L1) of turbine 10, or in only the first stage (L4), second stage (L3), third stage (L2), and fourth stage (L1) of turbine 10.

In various embodiments, at least one of endwalls 212 including contour 218 can include an inner endwall, e.g., a radially inner endwall configured to align on the radially inner side of the static nozzle section. In other embodiments, at least one of endwalls 212 including contour 218 can include an outer endwall, e.g., a radially outer endwall configured to align on the radially outer side of the static nozzle section. In some cases, both endwalls 212 include contour 218, and in other cases, only one of the endwalls 212 includes contour 218.

With reference to FIGS. 2 and 3, in various embodiments, axisymmetric contour 218 may include a bump 260 along endwall 212 on suction side 204 of airfoil 202. Bump 260 can have distinct slopes, e.g., distinct radial v. circumferential ratios. In some cases, bump 260 has a gradient that is positive or negative, but not equal to zero.

According to various particular embodiments, nozzle 200 has a first length L1 measured from a junction 228 of suction side 204 and leading edge 208 of airfoil 202 along endwall 212 to an outer edge 230 of endwall 212. In these embodiments, nozzle 200 has a second length L2 measured from a junction 232 of pressure side 206 and leading edge 208 of airfoil 202 along endwall 212 to an inner edge 234 of endwall 212. In various embodiments, first length L1 is distinct from second length L2, and in particular embodiments, second length L2 is greater than first length L1.

Turning to FIG. 3, nozzle 202 has a curved axisymmetric contour 218, shown according to various embodiments. FIG. 3 shows a comparison between a typical linear contour 280 and curved axisymmetric contour 218 according to various embodiments. Axisymmetric contour 218 is designed to meet surface loading distribution requirements on the suction side 204 of the nozzle 202. Axisymmetric contour 218 may include bump 260 according to various embodiments. Bump 260 may increase the annulus area of the plurality of nozzles 200. Bump 260 may locally suppress the flow velocity near the outer diameter flow path of nozzle 200 according to various embodiments.

In various particular embodiments, each bump (thickened area) 260 can extend across approximately at least 10 percent of axial length L_(A) (along axis A) of endwall 212. In some particular cases, each thickened area 260 can extend across approximately 20-30 percent of axial length L_(A) of endwall 212.

In various particular embodiments, at least one bump 260 on pressure side 206 can have an apex at approximately 50% of the axial chord downstream of leading edge 208 (+/−10%). In other particular embodiments, at least one bump 260 on suction side 204 can have apex at approximately 45-55% of the axial cord downstream of leading edge 208 (+/−10%). In these cases, bump 260 can extend across an entire pitch of nozzle 200. The pitch of the nozzle refers to the circumferential direction around nozzle 200, along suction side 204 from leading edge to trailing edge

It is understood that in various embodiments, other apex locations are possible, and those values given herein are merely illustrative of several of the many possible embodiments in accordance with the disclosure.

With reference to FIG. 4 (and continuing reference to FIGS. 2-3), a plurality of points 270-278 along span S, including root 215 and tip 217, can correspond to Z coordinate values of chord lines, and a cross section of airfoil 202 at each point can be described by a respective set of X and Y coordinates. For example, 100 points can be listed for each cross section 270-278, though it should be apparent that more or fewer points can be used for each cross section, and more or fewer cross sections can be used, as may be desired and/or appropriate. The X, Y, and Z coordinate values in TABLE I have been expressed in normalized or non-dimensionalized form in values of from 0 to 1, but it should be apparent that any or all of the coordinate values could instead be expressed in distance units so long as the proportions are maintained. To convert an X, Y or Z value of TABLE I to a respective X, Y or Z coordinate value in units of distance, such as inches or meters, the non-dimensional X, Y or Z value given in TABLE I can be multiplied by a leading edge height of airfoil 202 in such units of distance. By connecting the X and Y values with smooth continuing arcs, each profile cross section at each distance Z can be fixed, and the airfoil profiles of the various surface locations between the distances Z can be determined by smoothly connecting adjacent profile sections to one another, thus forming the airfoil profile.

The values in TABLE I are generated and shown to four decimal places for determining the profile of at least one of a suction side or a pressure side of a nominal airfoil 202 at ambient, non-operating, or non-hot conditions, and do not take any coatings or fillets into account, though embodiments could account for other conditions, coatings, and/or fillets. To allow for typical manufacturing tolerances and/or coating thicknesses, ±values can be added to the values listed in TABLE I, particularly to the X and Y values therein. For example, a tolerance of about 10-20 percent of a thickness of the trailing edge in a direction normal to any surface location along the airfoil profile can define an airfoil profile envelope for a nozzle airfoil design at cold or room temperature. In other words, a distance of about 10-20 percent of a thickness of the trailing edge in a direction normal to any surface location along the airfoil profile can define a range of variation between measured points on an actual airfoil surface and ideal positions of those points, particularly at a cold or room temperature, as embodied by the invention. The nozzle airfoil design, as embodied by the invention, is robust to this range of variation without impairment of mechanical and aerodynamic functions. Likewise, the profile and/or design can be scaled up or down, such as geometrically, without impairment of operation, and such scaling can be facilitated by use of normalized coordinate values, i.e. multiplying the normalized values by a scaling factor, or a larger or smaller number of distance units than might have originally been used. For example, the values in TABLE I, particularly the X and Y values, could be multiplied by a scaling factor of 2, 0.5, or any other desired scaling factor. Alternatively, the values could be multiplied by a larger or smaller desired span. As referenced herein, the origin of the X, Y, Z coordinate system is the root of the leading edge (junction 232) of airfoil 202.

TABLE I Non-Dimensionalized (X Y Z/Radial Height) N Location X Y Z 1 Pressure-Side 0.0000 0.0000 0 2 Pressure-Side 0.0989 0.5387 0 3 Pressure-Side 0.3313 0.9356 0 4 Pressure-Side 0.6789 1.2374 0 5 Pressure-Side 1.0916 1.4432 0 6 Pressure-Side 1.5325 1.5817 0 7 Pressure-Side 1.9853 1.6738 0 8 Pressure-Side 2.4432 1.7349 0 9 Pressure-Side 2.9033 1.7790 0 10 Pressure-Side 3.3646 1.8129 0 11 Pressure-Side 3.8259 1.8389 0 12 Pressure-Side 4.2877 1.8604 0 13 Pressure-Side 4.7496 1.8790 0 14 Pressure-Side 5.2109 1.8988 0 15 Pressure-Side 5.6727 1.9220 0 16 Pressure-Side 6.1340 1.9503 0 17 Pressure-Side 6.5953 1.9825 0 18 Pressure-Side 7.0560 2.0198 0 19 Pressure-Side 7.5161 2.0627 0 20 Pressure-Side 7.9757 2.1108 0 21 Pressure-Side 8.4347 2.1651 0 22 Pressure-Side 8.8932 2.2250 0 23 Pressure-Side 9.3505 2.2917 0 24 Pressure-Side 9.8067 2.3652 0 25 Pressure-Side 10.2617 2.4460 0 26 Pressure-Side 10.7157 2.5336 0 27 Pressure-Side 11.1679 2.6297 0 28 Pressure-Side 11.6179 2.7326 0 29 Pressure-Side 12.0667 2.8434 0 30 Pressure-Side 12.5138 2.9610 0 31 Pressure-Side 12.9587 3.0865 0 32 Pressure-Side 13.4014 3.2188 0 33 Pressure-Side 13.8423 3.3584 0 34 Pressure-Side 14.2804 3.5048 0 35 Pressure-Side 14.7162 3.6591 0 36 Pressure-Side 15.1492 3.8197 0 37 Pressure-Side 15.5800 3.9881 0 38 Pressure-Side 16.0079 4.1628 0 39 Pressure-Side 16.4330 4.3448 0 40 Pressure-Side 16.8547 4.5336 0 41 Pressure-Side 17.2736 4.7292 0 42 Pressure-Side 17.6891 4.9316 0 43 Pressure-Side 18.1012 5.1408 0 44 Pressure-Side 18.5099 5.3567 0 45 Pressure-Side 18.9152 5.5789 0 46 Pressure-Side 19.3166 5.8072 0 47 Pressure-Side 19.7145 6.0424 0 48 Pressure-Side 20.1091 6.2838 0 49 Pressure-Side 20.4992 6.5314 0 50 Pressure-Side 20.8858 6.7846 0 51 Pressure-Side 21.2679 7.0441 0 52 Pressure-Side 21.6467 7.3098 0 53 Pressure-Side 22.0204 7.5811 0 54 Pressure-Side 22.3906 7.8581 0 55 Pressure-Side 22.7564 8.1413 0 56 Pressure-Side 23.1176 8.4291 0 57 Pressure-Side 23.4743 8.7230 0 58 Pressure-Side 23.8270 9.0215 0 59 Pressure-Side 24.1752 9.3250 0 60 Pressure-Side 24.5195 9.6337 0 61 Pressure-Side 24.8592 9.9474 0 62 Pressure-Side 25.1945 10.2657 0 63 Pressure-Side 25.5257 10.5879 0 64 Pressure-Side 25.8519 10.9152 0 65 Pressure-Side 26.1747 11.2465 0 66 Pressure-Side 26.4924 11.5817 0 67 Pressure-Side 26.8061 11.9209 0 68 Pressure-Side 27.1159 12.2640 0 69 Pressure-Side 27.4217 12.6111 0 70 Pressure-Side 27.7230 12.9610 0 71 Pressure-Side 28.0209 13.3149 0 72 Pressure-Side 28.3149 13.6710 0 73 Pressure-Side 28.6054 14.0311 0 74 Pressure-Side 28.8920 14.3934 0 75 Pressure-Side 29.1752 14.7586 0 76 Pressure-Side 29.4551 15.1261 0 77 Pressure-Side 29.7321 15.4963 0 78 Pressure-Side 30.0051 15.8694 0 79 Pressure-Side 30.2753 16.2442 0 80 Pressure-Side 30.5427 16.6213 0 81 Pressure-Side 30.8067 17.0011 0 82 Pressure-Side 31.0678 17.3821 0 83 Pressure-Side 31.3267 17.7648 0 84 Pressure-Side 31.5828 18.1498 0 85 Pressure-Side 31.8372 18.5353 0 86 Pressure-Side 32.0893 18.9226 0 87 Pressure-Side 32.3403 19.3115 0 88 Pressure-Side 32.5890 19.7004 0 89 Pressure-Side 32.8366 20.0910 0 90 Pressure-Side 33.0820 20.4828 0 91 Pressure-Side 33.4579 20.6727 0 92 Suction-Side 33.6365 20.3002 0 93 Suction-Side 33.4257 19.8892 0 94 Suction-Side 33.2109 19.4799 0 95 Suction-Side 32.9966 19.0707 0 96 Suction-Side 32.7824 18.6608 0 97 Suction-Side 32.5681 18.2510 0 98 Suction-Side 32.3544 17.8417 0 99 Suction-Side 32.1402 17.4319 0 100 Suction-Side 31.9265 17.0220 0 101 Suction-Side 31.7128 16.6122 0 102 Suction-Side 31.4997 16.2024 0 103 Suction-Side 31.2860 15.7925 0 104 Suction-Side 31.0729 15.3821 0 105 Suction-Side 30.8598 14.9723 0 106 Suction-Side 30.6467 14.5619 0 107 Suction-Side 30.4330 14.1521 0 108 Suction-Side 30.2199 13.7422 0 109 Suction-Side 30.0062 13.3324 0 110 Suction-Side 29.7925 12.9226 0 111 Suction-Side 29.5783 12.5127 0 112 Suction-Side 29.3635 12.1034 0 113 Suction-Side 29.1487 11.6942 0 114 Suction-Side 28.9333 11.2855 0 115 Suction-Side 28.7174 10.8768 0 116 Suction-Side 28.5008 10.4686 0 117 Suction-Side 28.2832 10.0605 0 118 Suction-Side 28.0650 9.6535 0 119 Suction-Side 27.8451 9.2465 0 120 Suction-Side 27.6246 8.8406 0 121 Suction-Side 27.4031 8.4347 0 122 Suction-Side 27.1798 8.0300 0 123 Suction-Side 26.9548 7.6263 0 124 Suction-Side 26.7281 7.2233 0 125 Suction-Side 26.4997 6.8219 0 126 Suction-Side 26.2696 6.4211 0 127 Suction-Side 26.0367 6.0215 0 128 Suction-Side 25.8021 5.6235 0 129 Suction-Side 25.5653 5.2267 0 130 Suction-Side 25.3256 4.8315 0 131 Suction-Side 25.0831 4.4381 0 132 Suction-Side 24.8372 4.0464 0 133 Suction-Side 24.5879 3.6574 0 134 Suction-Side 24.3352 3.2702 0 135 Suction-Side 24.0786 2.8858 0 136 Suction-Side 23.8180 2.5042 0 137 Suction-Side 23.5534 2.1249 0 138 Suction-Side 23.2843 1.7490 0 139 Suction-Side 23.0113 1.3765 0 140 Suction-Side 22.7326 1.0079 0 141 Suction-Side 22.4494 0.6427 0 142 Suction-Side 22.1611 0.2815 0 143 Suction-Side 21.8666 −0.0752 0 144 Suction-Side 21.5670 −0.4268 0 145 Suction-Side 21.2606 −0.7733 0 146 Suction-Side 20.9486 −1.1136 0 147 Suction-Side 20.6297 −1.4483 0 148 Suction-Side 20.3041 −1.7767 0 149 Suction-Side 19.9717 −2.0978 0 150 Suction-Side 19.6326 −2.4115 0 151 Suction-Side 19.2860 −2.7174 0 152 Suction-Side 18.9322 −3.0147 0 153 Suction-Side 18.5715 −3.3036 0 154 Suction-Side 18.2029 −3.5828 0 155 Suction-Side 17.8276 −3.8525 0 156 Suction-Side 17.4449 −4.1114 0 157 Suction-Side 17.0548 −4.3595 0 158 Suction-Side 16.6574 −4.5958 0 159 Suction-Side 16.2533 −4.8197 0 160 Suction-Side 15.8428 −5.0317 0 161 Suction-Side 15.4251 −5.2301 0 162 Suction-Side 15.0017 −5.4149 0 163 Suction-Side 14.5721 −5.5856 0 164 Suction-Side 14.1374 −5.7417 0 165 Suction-Side 13.6970 −5.8836 0 166 Suction-Side 13.2527 −6.0096 0 167 Suction-Side 12.8038 −6.1204 0 168 Suction-Side 12.3516 −6.2154 0 169 Suction-Side 11.8966 −6.2945 0 170 Suction-Side 11.4387 −6.3573 0 171 Suction-Side 10.9785 −6.4036 0 172 Suction-Side 10.5172 −6.4330 0 173 Suction-Side 10.0554 −6.4460 0 174 Suction-Side 9.5930 −6.4426 0 175 Suction-Side 9.1317 −6.4223 0 176 Suction-Side 8.6710 −6.3850 0 177 Suction-Side 8.2120 −6.3313 0 178 Suction-Side 7.7552 −6.2600 0 179 Suction-Side 7.3013 −6.1724 0 180 Suction-Side 6.8508 −6.0684 0 181 Suction-Side 6.4047 −5.9474 0 182 Suction-Side 5.9638 −5.8095 0 183 Suction-Side 5.5280 −5.6552 0 184 Suction-Side 5.0984 −5.4850 0 185 Suction-Side 4.6761 −5.2979 0 186 Suction-Side 4.2612 −5.0944 0 187 Suction-Side 3.8547 −4.8739 0 188 Suction-Side 3.4579 −4.6371 0 189 Suction-Side 3.0712 −4.3844 0 190 Suction-Side 2.6953 −4.1153 0 191 Suction-Side 2.3318 −3.8298 0 192 Suction-Side 1.9825 −3.5274 0 193 Suction-Side 1.6490 −3.2075 0 194 Suction-Side 1.3335 −2.8694 0 195 Suction-Side 1.0373 −2.5144 0 196 Suction-Side 0.7648 −2.1419 0 197 Suction-Side 0.5201 −1.7496 0 198 Suction-Side 0.3098 −1.3380 0 199 Suction-Side 0.1419 −0.9079 0 200 Suction-Side 0.0317 −0.4596 0 1 Pressure-Side −0.6015 −1.7151 10 2 Pressure-Side −0.4941 −1.2442 10 3 Pressure-Side −0.2442 −0.8321 10 4 Pressure-Side 0.1317 −0.5285 10 5 Pressure-Side 0.5659 −0.3143 10 6 Pressure-Side 1.0243 −0.1588 10 7 Pressure-Side 1.4952 −0.0447 10 8 Pressure-Side 1.9712 0.0469 10 9 Pressure-Side 2.4500 0.1244 10 10 Pressure-Side 2.9299 0.1911 10 11 Pressure-Side 3.4110 0.2521 10 12 Pressure-Side 3.8920 0.3103 10 13 Pressure-Side 4.3731 0.3674 10 14 Pressure-Side 4.8547 0.4245 10 15 Pressure-Side 5.3358 0.4828 10 16 Pressure-Side 5.8163 0.5432 10 17 Pressure-Side 6.2968 0.6071 10 18 Pressure-Side 6.7767 0.6755 10 19 Pressure-Side 7.2561 0.7484 10 20 Pressure-Side 7.7343 0.8265 10 21 Pressure-Side 8.2120 0.9090 10 22 Pressure-Side 8.6885 0.9966 10 23 Pressure-Side 9.1645 1.0893 10 24 Pressure-Side 9.6388 1.1877 10 25 Pressure-Side 10.1119 1.2917 10 26 Pressure-Side 10.5845 1.4019 10 27 Pressure-Side 11.0548 1.5172 10 28 Pressure-Side 11.5240 1.6393 10 29 Pressure-Side 11.9915 1.7682 10 30 Pressure-Side 12.4568 1.9028 10 31 Pressure-Side 12.9203 2.0441 10 32 Pressure-Side 13.3821 2.1922 10 33 Pressure-Side 13.8417 2.3460 10 34 Pressure-Side 14.2990 2.5065 10 35 Pressure-Side 14.7541 2.6733 10 36 Pressure-Side 15.2063 2.8468 10 37 Pressure-Side 15.6569 3.0260 10 38 Pressure-Side 16.1040 3.2120 10 39 Pressure-Side 16.5489 3.4047 10 40 Pressure-Side 16.9910 3.6037 10 41 Pressure-Side 17.4302 3.8089 10 42 Pressure-Side 17.8660 4.0204 10 43 Pressure-Side 18.2990 4.2386 10 44 Pressure-Side 18.7287 4.4630 10 45 Pressure-Side 19.1549 4.6936 10 46 Pressure-Side 19.5777 4.9305 10 47 Pressure-Side 19.9972 5.1735 10 48 Pressure-Side 20.4127 5.4228 10 49 Pressure-Side 20.8248 5.6783 10 50 Pressure-Side 21.2329 5.9395 10 51 Pressure-Side 21.6371 6.2069 10 52 Pressure-Side 22.0373 6.4805 10 53 Pressure-Side 22.4330 6.7598 10 54 Pressure-Side 22.8253 7.0447 10 55 Pressure-Side 23.2131 7.3352 10 56 Pressure-Side 23.5964 7.6320 10 57 Pressure-Side 23.9751 7.9339 10 58 Pressure-Side 24.3499 8.2414 10 59 Pressure-Side 24.7202 8.5540 10 60 Pressure-Side 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Pressure-Side −1.3737 −12.1114 90 11 Pressure-Side −0.7705 −11.8609 90 12 Pressure-Side −0.1634 −11.6207 90 13 Pressure-Side 0.4454 −11.3861 90 14 Pressure-Side 1.0560 −11.1549 90 15 Pressure-Side 1.6676 −10.9265 90 16 Pressure-Side 2.2804 −10.7010 90 17 Pressure-Side 2.8932 −10.4760 90 18 Pressure-Side 3.5065 −10.2521 90 19 Pressure-Side 4.1198 −10.0283 90 20 Pressure-Side 4.7326 −9.8027 90 21 Pressure-Side 5.3448 −9.5760 90 22 Pressure-Side 5.9565 −9.3477 90 23 Pressure-Side 6.5670 −9.1170 90 24 Pressure-Side 7.1769 −8.8841 90 25 Pressure-Side 7.7858 −8.6490 90 26 Pressure-Side 8.3940 −8.4110 90 27 Pressure-Side 9.0006 −8.1702 90 28 Pressure-Side 9.6066 −7.9265 90 29 Pressure-Side 10.2109 −7.6800 90 30 Pressure-Side 10.8140 −7.4296 90 31 Pressure-Side 11.4155 −7.1758 90 32 Pressure-Side 12.0153 −6.9180 90 33 Pressure-Side 12.6133 −6.6563 90 34 Pressure-Side 13.2097 −6.3906 90 35 Pressure-Side 13.8044 −6.1215 90 36 Pressure-Side 14.3974 −5.8479 90 37 Pressure-Side 14.9881 −5.5709 90 38 Pressure-Side 15.5777 −5.2894 90 39 Pressure-Side 16.1645 −5.0040 90 40 Pressure-Side 16.7496 −4.7145 90 41 Pressure-Side 17.3330 −4.4211 90 42 Pressure-Side 17.9141 −4.1238 90 43 Pressure-Side 18.4929 −3.8214 90 44 Pressure-Side 19.0695 −3.5155 90 45 Pressure-Side 19.6439 −3.2052 90 46 Pressure-Side 20.2159 −2.8903 90 47 Pressure-Side 20.7858 −2.5715 90 48 Pressure-Side 21.3527 −2.2487 90 49 Pressure-Side 21.9175 −1.9214 90 50 Pressure-Side 22.4799 −1.5896 90 51 Pressure-Side 23.0396 −1.2533 90 52 Pressure-Side 23.5969 −0.9129 90 53 Pressure-Side 24.1515 −0.5687 90 54 Pressure-Side 24.7032 −0.2193 90 55 Pressure-Side 25.2521 0.1340 90 56 Pressure-Side 25.7982 0.4918 90 57 Pressure-Side 26.3409 0.8542 90 58 Pressure-Side 26.8813 1.2210 90 59 Pressure-Side 27.4183 1.5919 90 60 Pressure-Side 27.9520 1.9678 90 61 Pressure-Side 28.4828 2.3482 90 62 Pressure-Side 29.0102 2.7326 90 63 Pressure-Side 29.5342 3.1221 90 64 Pressure-Side 30.0548 3.5161 90 65 Pressure-Side 30.5721 3.9146 90 66 Pressure-Side 31.0859 4.3171 90 67 Pressure-Side 31.5958 4.7247 90 68 Pressure-Side 32.1023 5.1368 90 69 Pressure-Side 32.6049 5.5540 90 70 Pressure-Side 33.1034 5.9751 90 71 Pressure-Side 33.5981 6.4014 90 72 Pressure-Side 34.0882 6.8321 90 73 Pressure-Side 34.5749 7.2679 90 74 Pressure-Side 35.0565 7.7083 90 75 Pressure-Side 35.5336 8.1538 90 76 Pressure-Side 36.0057 8.6043 90 77 Pressure-Side 36.4737 9.0599 90 78 Pressure-Side 36.9361 9.5212 90 79 Pressure-Side 37.3934 9.9870 90 80 Pressure-Side 37.8451 10.4579 90 81 Pressure-Side 38.2917 10.9344 90 82 Pressure-Side 38.7326 11.4161 90 83 Pressure-Side 39.1673 11.9028 90 84 Pressure-Side 39.5969 12.3946 90 85 Pressure-Side 40.0204 12.8909 90 86 Pressure-Side 40.4392 13.3923 90 87 Pressure-Side 40.8525 13.8971 90 88 Pressure-Side 41.2617 14.4064 90 89 Pressure-Side 41.6659 14.9186 90 90 Pressure-Side 42.0673 15.4341 90 91 Pressure-Side 42.4652 15.9514 90 92 Pressure-Side 42.8615 16.4698 90 93 Pressure-Side 43.2566 16.9898 90 94 Pressure-Side 43.6851 17.4698 90 95 Suction-Side 43.9938 17.0577 90 96 Suction-Side 43.9938 17.0577 90 97 Suction-Side 43.6902 16.4799 90 98 Suction-Side 43.3867 15.9016 90 99 Suction-Side 43.0825 15.3239 90 100 Suction-Side 42.7778 14.7467 90 101 Suction-Side 42.4731 14.1690 90 102 Suction-Side 42.1673 13.5924 90 103 Suction-Side 41.8604 13.0164 90 104 Suction-Side 41.5523 12.4404 90 105 Suction-Side 41.2431 11.8655 90 106 Suction-Side 40.9327 11.2911 90 107 Suction-Side 40.6207 10.7179 90 108 Suction-Side 40.3075 10.1453 90 109 Suction-Side 39.9921 9.5732 90 110 Suction-Side 39.6750 9.0028 90 111 Suction-Side 39.3561 8.4330 90 112 Suction-Side 39.0350 7.8649 90 113 Suction-Side 38.7117 7.2973 90 114 Suction-Side 38.3861 6.7315 90 115 Suction-Side 38.0582 6.1673 90 116 Suction-Side 37.7275 5.6043 90 117 Suction-Side 37.3946 5.0430 90 118 Suction-Side 37.0582 4.4828 90 119 Suction-Side 36.7196 3.9248 90 120 Suction-Side 36.3782 3.3686 90 121 Suction-Side 36.0334 2.8140 90 122 Suction-Side 35.6851 2.2617 90 123 Suction-Side 35.3341 1.7117 90 124 Suction-Side 34.9791 1.1634 90 125 Suction-Side 34.6213 0.6179 90 126 Suction-Side 34.2589 0.0746 90 127 Suction-Side 33.8932 −0.4664 90 128 Suction-Side 33.5229 −1.0040 90 129 Suction-Side 33.1492 −1.5393 90 130 Suction-Side 32.7705 −2.0712 90 131 Suction-Side 32.3884 −2.6003 90 132 Suction-Side 32.0011 −3.1261 90 133 Suction-Side 31.6094 −3.6484 90 134 Suction-Side 31.2131 −4.1673 90 135 Suction-Side 30.8118 −4.6823 90 136 Suction-Side 30.4053 −5.1933 90 137 Suction-Side 29.9938 −5.6998 90 138 Suction-Side 29.5772 −6.2024 90 139 Suction-Side 29.1549 −6.7004 90 140 Suction-Side 28.7270 −7.1933 90 141 Suction-Side 28.2928 −7.6812 90 142 Suction-Side 27.8530 −8.1639 90 143 Suction-Side 27.4076 −8.6405 90 144 Suction-Side 26.9559 −9.1119 90 145 Suction-Side 26.4975 −9.5772 90 146 Suction-Side 26.0334 −10.0362 90 147 Suction-Side 25.5625 −10.4884 90 148 Suction-Side 25.0848 −10.9333 90 149 Suction-Side 24.6009 −11.3714 90 150 Suction-Side 24.1102 −11.8021 90 151 Suction-Side 23.6128 −12.2250 90 152 Suction-Side 23.1085 −12.6393 90 153 Suction-Side 22.5975 −13.0458 90 154 Suction-Side 22.0791 −13.4432 90 155 Suction-Side 21.5546 −13.8315 90 156 Suction-Side 21.0232 −14.2103 90 157 Suction-Side 20.4845 −14.5794 90 158 Suction-Side 19.9395 −14.9389 90 159 Suction-Side 19.3872 −15.2872 90 160 Suction-Side 18.8287 −15.6252 90 161 Suction-Side 18.2640 −15.9525 90 162 Suction-Side 17.6925 −16.2679 90 163 Suction-Side 17.1148 −16.5721 90 164 Suction-Side 16.5308 −16.8643 90 165 Suction-Side 15.9412 −17.1441 90 166 Suction-Side 15.3460 −17.4121 90 167 Suction-Side 14.7451 −17.6670 90 168 Suction-Side 14.1385 −17.9096 90 169 Suction-Side 13.5274 −18.1385 90 170 Suction-Side 12.9112 −18.3550 90 171 Suction-Side 12.2911 −18.5579 90 172 Suction-Side 11.6665 −18.7479 90 173 Suction-Side 11.0379 −18.9243 90 174 Suction-Side 10.4053 −19.0865 90 175 Suction-Side 9.7699 −19.2352 90 176 Suction-Side 9.1306 −19.3691 90 177 Suction-Side 8.4890 −19.4884 90 178 Suction-Side 7.8445 −19.5930 90 179 Suction-Side 7.1979 −19.6823 90 180 Suction-Side 6.5495 −19.7569 90 181 Suction-Side 5.8994 −19.8163 90 182 Suction-Side 5.2476 −19.8598 90 183 Suction-Side 4.5958 −19.8886 90 184 Suction-Side 3.9429 −19.9005 90 185 Suction-Side 3.2900 −19.8954 90 186 Suction-Side 2.6376 −19.8728 90 187 Suction-Side 1.9859 −19.8315 90 188 Suction-Side 1.3363 −19.7705 90 189 Suction-Side 0.6885 −19.6891 90 190 Suction-Side 0.0441 −19.5856 90 191 Suction-Side −0.5964 −19.4568 90 192 Suction-Side −1.2301 −19.3019 90 193 Suction-Side −1.8564 −19.1164 90 194 Suction-Side −2.4709 −18.8960 90 195 Suction-Side −3.0690 −18.6360 90 196 Suction-Side −3.6450 −18.3284 90 197 Suction-Side −4.1854 −17.9633 90 198 Suction-Side −4.6733 −17.5302 90 199 Suction-Side −5.0786 −17.0198 90 200 Suction-Side −5.3686 −16.4364 90 1 Pressure-Side −6.1142 −17.3431 100 2 Pressure-Side −6.1142 −17.3431 100 3 Pressure-Side −5.9977 −16.6829 100 4 Pressure-Side −5.6620 −16.1006 100 5 Pressure-Side −5.1945 −15.6150 100 6 Pressure-Side −4.6631 −15.2001 100 7 Pressure-Side −4.0955 −14.8361 100 8 Pressure-Side −3.5054 −14.5088 100 9 Pressure-Side −2.9045 −14.2024 100 10 Pressure-Side −2.2951 −13.9124 100 11 Pressure-Side −1.6800 −13.6354 100 12 Pressure-Side −1.0605 −13.3686 100 13 Pressure-Side −0.4375 −13.1097 100 14 Pressure-Side 0.1877 −12.8553 100 15 Pressure-Side 0.8135 −12.6026 100 16 Pressure-Side 1.4392 −12.3522 100 17 Pressure-Side 2.0661 −12.1023 100 18 Pressure-Side 2.6936 −11.8536 100 19 Pressure-Side 3.3211 −11.6054 100 20 Pressure-Side 3.9486 −11.3578 100 21 Pressure-Side 4.5760 −11.1097 100 22 Pressure-Side 5.2029 −10.8609 100 23 Pressure-Side 5.8298 −10.6111 100 24 Pressure-Side 6.4562 −10.3601 100 25 Pressure-Side 7.0814 −10.1074 100 26 Pressure-Side 7.7066 −9.8530 100 27 Pressure-Side 8.3301 −9.5958 100 28 Pressure-Side 8.9531 −9.3363 100 29 Pressure-Side 9.5749 −9.0746 100 30 Pressure-Side 10.1956 −8.8101 100 31 Pressure-Side 10.8146 −8.5427 100 32 Pressure-Side 11.4330 −8.2730 100 33 Pressure-Side 12.0503 −8.0000 100 34 Pressure-Side 12.6659 −7.7241 100 35 Pressure-Side 13.2804 −7.4449 100 36 Pressure-Side 13.8932 −7.1628 100 37 Pressure-Side 14.5042 −6.8773 100 38 Pressure-Side 15.1136 −6.5879 100 39 Pressure-Side 15.7219 −6.2951 100 40 Pressure-Side 16.3279 −5.9989 100 41 Pressure-Side 16.9322 −5.6987 100 42 Pressure-Side 17.5342 −5.3946 100 43 Pressure-Side 18.1345 −5.0865 100 44 Pressure-Side 18.7326 −4.7744 100 45 Pressure-Side 19.3284 −4.4585 100 46 Pressure-Side 19.9226 −4.1385 100 47 Pressure-Side 20.5138 −3.8140 100 48 Pressure-Side 21.1034 −3.4850 100 49 Pressure-Side 21.6902 −3.1521 100 50 Pressure-Side 22.2742 −2.8151 100 51 Pressure-Side 22.8564 −2.4731 100 52 Pressure-Side 23.4353 −2.1272 100 53 Pressure-Side 24.0113 −1.7761 100 54 Pressure-Side 24.5851 −1.4211 100 55 Pressure-Side 25.1560 −1.0611 100 56 Pressure-Side 25.7236 −0.6970 100 57 Pressure-Side 26.2883 −0.3279 100 58 Pressure-Side 26.8502 0.0458 100 59 Pressure-Side 27.4087 0.4240 100 60 Pressure-Side 27.9644 0.8072 100 61 Pressure-Side 28.5167 1.1945 100 62 Pressure-Side 29.0656 1.5868 100 63 Pressure-Side 29.6111 1.9842 100 64 Pressure-Side 30.1532 2.3861 100 65 Pressure-Side 30.6914 2.7925 100 66 Pressure-Side 31.2261 3.2035 100 67 Pressure-Side 31.7569 3.6201 100 68 Pressure-Side 32.2843 4.0407 100 69 Pressure-Side 32.8078 4.4664 100 70 Pressure-Side 33.3273 4.8971 100 71 Pressure-Side 33.8428 5.3324 100 72 Pressure-Side 34.3539 5.7728 100 73 Pressure-Side 34.8609 6.2182 100 74 Pressure-Side 35.3635 6.6682 100 75 Pressure-Side 35.8615 7.1232 100 76 Pressure-Side 36.3556 7.5828 100 77 Pressure-Side 36.8445 8.0475 100 78 Pressure-Side 37.3284 8.5172 100 79 Pressure-Side 37.8072 8.9927 100 80 Pressure-Side 38.2815 9.4726 100 81 Pressure-Side 38.7501 9.9582 100 82 Pressure-Side 39.2137 10.4483 100 83 Pressure-Side 39.6727 10.9429 100 84 Pressure-Side 40.1261 11.4426 100 85 Pressure-Side 40.5743 11.9463 100 86 Pressure-Side 41.0175 12.4551 100 87 Pressure-Side 41.4562 12.9683 100 88 Pressure-Side 41.8892 13.4856 100 89 Pressure-Side 42.3171 14.0068 100 90 Pressure-Side 42.7411 14.5319 100 91 Pressure-Side 43.1611 15.0599 100 92 Pressure-Side 43.5789 15.5896 100 93 Pressure-Side 43.9943 16.1215 100 94 Pressure-Side 44.4081 16.6540 100 95 Pressure-Side 44.8672 17.1283 100 96 Suction-Side 45.1272 16.6574 100 97 Suction-Side 44.8101 16.0616 100 98 Suction-Side 44.4958 15.4652 100 99 Suction-Side 44.1803 14.8683 100 100 Suction-Side 43.8649 14.2725 100 101 Suction-Side 43.5483 13.6767 100 102 Suction-Side 43.2306 13.0814 100 103 Suction-Side 42.9112 12.4867 100 104 Suction-Side 42.5907 11.8932 100 105 Suction-Side 42.2691 11.3002 100 106 Suction-Side 41.9452 10.7083 100 107 Suction-Side 41.6196 10.1176 100 108 Suction-Side 41.2923 9.5274 100 109 Suction-Side 40.9633 8.9384 100 110 Suction-Side 40.6320 8.3510 100 111 Suction-Side 40.2985 7.7643 100 112 Suction-Side 39.9627 7.1792 100 113 Suction-Side 39.6241 6.5953 100 114 Suction-Side 39.2832 6.0130 100 115 Suction-Side 38.9401 5.4324 100 116 Suction-Side 38.5941 4.8530 100 117 Suction-Side 38.2448 4.2759 100 118 Suction-Side 37.8932 3.7004 100 119 Suction-Side 37.5382 3.1266 100 120 Suction-Side 37.1803 2.5546 100 121 Suction-Side 36.8191 1.9847 100 122 Suction-Side 36.4545 1.4172 100 123 Suction-Side 36.0859 0.8519 100 124 Suction-Side 35.7145 0.2883 100 125 Suction-Side 35.3392 −0.2719 100 126 Suction-Side 34.9604 −0.8304 100 127 Suction-Side 34.5772 −1.3861 100 128 Suction-Side 34.1905 −1.9384 100 129 Suction-Side 33.7999 −2.4884 100 130 Suction-Side 33.4047 −3.0356 100 131 Suction-Side 33.0051 −3.5789 100 132 Suction-Side 32.6009 −4.1193 100 133 Suction-Side 32.1922 −4.6563 100 134 Suction-Side 31.7784 −5.1894 100 135 Suction-Side 31.3601 −5.7185 100 136 Suction-Side 30.9361 −6.2431 100 137 Suction-Side 30.5076 −6.7643 100 138 Suction-Side 30.0735 −7.2804 100 139 Suction-Side 29.6337 −7.7925 100 140 Suction-Side 29.1882 −8.2990 100 141 Suction-Side 28.7371 −8.8010 100 142 Suction-Side 28.2798 −9.2968 100 143 Suction-Side 27.8168 −9.7875 100 144 Suction-Side 27.3471 −10.2719 100 145 Suction-Side 26.8711 −10.7501 100 146 Suction-Side 26.3889 −11.2216 100 147 Suction-Side 25.8999 −11.6863 100 148 Suction-Side 25.4042 −12.1441 100 149 Suction-Side 24.9016 −12.5947 100 150 Suction-Side 24.3929 −13.0373 100 151 Suction-Side 23.8768 −13.4715 100 152 Suction-Side 23.3533 −13.8977 100 153 Suction-Side 22.8236 −14.3154 100 154 Suction-Side 22.2860 −14.7236 100 155 Suction-Side 21.7422 −15.1221 100 156 Suction-Side 21.1911 −15.5116 100 157 Suction-Side 20.6331 −15.8909 100 158 Suction-Side 20.0684 −16.2595 100 159 Suction-Side 19.4963 −16.6179 100 160 Suction-Side 18.9180 −16.9650 100 161 Suction-Side 18.3330 −17.3013 100 162 Suction-Side 17.7417 −17.6258 100 163 Suction-Side 17.1436 −17.9389 100 164 Suction-Side 16.5399 −18.2397 100 165 Suction-Side 15.9299 −18.5280 100 166 Suction-Side 15.3149 −18.8050 100 167 Suction-Side 14.6942 −19.0690 100 168 Suction-Side 14.0678 −19.3205 100 169 Suction-Side 13.4370 −19.5591 100 170 Suction-Side 12.8010 −19.7846 100 171 Suction-Side 12.1605 −19.9972 100 172 Suction-Side 11.5161 −20.1962 100 173 Suction-Side 10.8677 −20.3821 100 174 Suction-Side 10.2154 −20.5546 100 175 Suction-Side 9.5596 −20.7134 100 176 Suction-Side 8.9005 −20.8587 100 177 Suction-Side 8.2391 −20.9898 100 178 Suction-Side 7.5743 −21.1068 100 179 Suction-Side 6.9079 −21.2097 100 180 Suction-Side 6.2386 −21.2979 100 181 Suction-Side 5.5681 −21.3708 100 182 Suction-Side 4.8960 −21.4291 100 183 Suction-Side 4.2227 −21.4720 100 184 Suction-Side 3.5483 −21.4980 100 185 Suction-Side 2.8739 −21.5071 100 186 Suction-Side 2.1995 −21.4986 100 187 Suction-Side 1.5252 −21.4715 100 188 Suction-Side 0.8519 −21.4251 100 189 Suction-Side 0.1809 −21.3578 100 190 Suction-Side −0.4873 −21.2668 100 191 Suction-Side −1.1515 −21.1481 100 192 Suction-Side −1.8101 −21.0000 100 193 Suction-Side −2.4596 −20.8197 100 194 Suction-Side −3.0984 −20.6020 100 195 Suction-Side −3.7196 −20.3386 100 196 Suction-Side −4.3137 −20.0204 100 197 Suction-Side −4.8683 −19.6365 100 198 Suction-Side −5.3595 −19.1752 100 199 Suction-Side −5.7541 −18.6297 100 200 Suction-Side −6.0130 −18.0085 100

Turning to FIG. 5, a schematic view of portions of a multi-shaft combined cycle power plant 900 is shown. Combined cycle power plant 900 may include, for example, a gas turbine 980 operably connected to a generator 970. Generator 970 and gas turbine 980 may be mechanically coupled by a shaft 915, which may transfer energy between a drive shaft (not shown) of gas turbine 980 and generator 970. Also shown in FIG. 5 is a heat exchanger 986 operably connected to gas turbine 980 and a steam turbine 992. Heat exchanger 986 may be fluidly connected to both gas turbine 980 and a steam turbine 992 via conventional conduits (numbering omitted). Gas turbine 980 and/or steam turbine 992 may include one or more nozzles 200 as shown and described with reference to FIG. 2 and/or other embodiments described herein. Heat exchanger 986 may be a conventional heat recovery steam generator (HRSG), such as those used in conventional combined cycle power systems. As is known in the art of power generation, HRSG 986 may use hot exhaust from gas turbine 980, combined with a water supply, to create steam which is fed to steam turbine 992. Steam turbine 992 may optionally be coupled to a second generator system 970 (via a second shaft 915). It is understood that generators 970 and shafts 915 may be of any size or type known in the art and may differ depending upon their application or the system to which they are connected. Common numbering of the generators and shafts is for clarity and does not necessarily suggest these generators or shafts are identical. In another embodiment, shown in FIG. 6, a single shaft combined cycle power plant 990 may include a single generator 970 coupled to both gas turbine 980 and steam turbine 992 via a single shaft 915. Steam turbine 992 and/or gas turbine 980 may include one or more nozzles 200 shown and described with reference to FIG. 2 and/or other embodiments described herein.

The apparatus and devices of the present disclosure are not limited to any one particular engine, turbine, jet engine, generator, power generation system or other system, and may be used with other aircraft systems, power generation systems and/or systems (e.g., combined cycle, simple cycle, nuclear reactor, etc.). Additionally, the apparatus of the present invention may be used with other systems not described herein that may benefit from the increased reduced tip leakage and increased efficiency of the apparatus and devices described herein.

In various embodiments, components described as being “coupled” to one another can be joined along one or more interfaces. In some embodiments, these interfaces can include junctions between distinct components, and in other cases, these interfaces can include a solidly and/or integrally formed interconnection. That is, in some cases, components that are “coupled” to one another can be simultaneously formed to define a single continuous member. However, in other embodiments, these coupled components can be formed as separate members and be subsequently joined through known processes (e.g., fastening, ultrasonic welding, bonding).

The terminology used herein is for the purpose of describing particular example embodiments only and is not intended to be limiting. As used herein, the singular forms “a”, “an” and “the” may be intended to include the plural forms as well, unless the context clearly indicates otherwise. The terms “comprises,” “comprising,” “including,” and “having,” are inclusive and therefore specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. The method steps, processes, and operations described herein are not to be construed as necessarily requiring their performance in the particular order discussed or illustrated, unless specifically identified as an order of performance. It is also to be understood that additional or alternative steps may be employed.

When an element or layer is referred to as being “on”, “engaged to”, “connected to” or “coupled to” another element or layer, it may be directly on, engaged, connected or coupled to the other element or layer, or intervening elements or layers may be present. In contrast, when an element is referred to as being “directly on,” “directly engaged to”, “directly connected to” or “directly coupled to” another element or layer, there may be no intervening elements or layers present. Other words used to describe the relationship between elements should be interpreted in a like fashion (e.g., “between” versus “directly between,” “adjacent” versus “directly adjacent,” etc.). As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items.

Spatially relative terms, such as “inner,” “outer,” “beneath”, “below”, “lower”, “above”, “upper” and the like, may be used herein for ease of description to describe one element or feature's relationship to another element(s) or feature(s) as illustrated in the figures. Spatially relative terms may be intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. For example, if the device in the figures is turned over, elements described as “below” or “beneath” other elements or features would then be oriented “above” the other elements or features. Thus, the example term “below” can encompass both an orientation of above and below. The device may be otherwise oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly.

The foregoing description of various aspects of the invention has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed, and obviously, many modifications and variations are possible. Such modifications and variations that may be apparent to an individual in the art are included within the scope of the invention as defined by the accompanying claims.

This written description uses examples to disclose the invention, including the best mode, and also to enable any person skilled in the art to practice the invention, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the invention is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal languages of the claims. 

We claim:
 1. A turbine nozzle comprising: an airfoil having: a suction side; a pressure side opposing the suction side; a leading edge spanning between the pressure side and the suction side; and a trailing edge opposing the leading edge and spanning between the pressure side and the suction side; and at least one endwall connected with the airfoil along the suction side, pressure side, trailing edge and the leading edge, the at least one endwall including an axisymmetric contour.
 2. The turbine nozzle of claim 1, further comprising a fillet connecting a surface of the endwall to a surface of the airfoil.
 3. The turbine nozzle of claim 1, wherein the turbine nozzle includes a fourth stage nozzle.
 4. The turbine nozzle of claim 1, wherein the at least one endwall directs flow of a working fluid through the axisymmetric contour.
 5. The turbine nozzle of claim 1, wherein the at least one endwall includes an inner endwall or an outer endwall.
 6. The turbine nozzle of claim 1, wherein the axisymmetric contour includes a thickened area having an apex at approximately 50% axial chord downstream of the leading edge.
 7. The turbine nozzle of claim 6, wherein the thickened area extends across at least approximately 10 percent of an axial length of the endwall, and extends across an entire pitch of the turbine nozzle.
 8. The turbine nozzle of claim 6, wherein the thickened area extends across approximately 20 percent to approximately 30 percent of an axial length of the endwall.
 9. The turbine nozzle of claim 1, wherein at least one of the suction side or the pressure side of the airfoil includes a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in TABLE I, wherein the coordinate values are non-dimensional values of from 0 to 1 convertible to distances by multiplying the values by a leading edge height expressed in units of distance, and wherein X and Y values connected by smooth continuing arcs define airfoil profile sections at each distance Z along the airfoil, the profile sections at the Z distances being joined smoothly with one another to form the airfoil profile, wherein the Cartesian coordinate values have an origin at a root of the leading edge of the airfoil.
 10. A static nozzle section comprising: a set of static nozzles, the set of static nozzles including at least one nozzle having: an airfoil having: a suction side; a pressure side opposing the suction side; a leading edge spanning between the pressure side and the suction side; and a trailing edge opposing the leading edge and spanning between the pressure side and the suction side; and at least one endwall connected with the airfoil along the suction side, pressure side, trailing edge and the leading edge, the at least one endwall including an axisymmetric contour, wherein at least one of the suction side or the pressure side of the airfoil includes a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in TABLE I, wherein the coordinate values are non-dimensional values of from 0 to 1 convertible to distances by multiplying the values by a leading edge height expressed in units of distance, and wherein X and Y values connected by smooth continuing arcs define airfoil profile sections at each distance Z along the airfoil, the profile sections at the Z distances being joined smoothly with one another to form the airfoil profile, wherein the Cartesian coordinate values have an origin at a root of the leading edge of the airfoil.
 11. The static nozzle section of claim 10, further comprising a fillet connecting a surface of the endwall to a surface of the airfoil.
 12. The static nozzle section of claim 10, wherein the turbine nozzle includes a fourth stage nozzle.
 13. The static nozzle section of claim 10, wherein the axisymmetric contour includes a thickened area having an apex at approximately 50% axial chord downstream of the leading edge.
 14. The static nozzle section of claim 13, wherein the thickened area extends across at least approximately 10 percent of an axial length of the endwall, and extends across an entire pitch of the turbine nozzle.
 15. The static nozzle section of claim 13, wherein the thickened area extends across approximately 20 percent to approximately 30 percent of an axial length of the endwall.
 16. The static nozzle section of claim 10, wherein the at least one endwall directs flow of a working fluid through the axisymmetric contour.
 17. A turbine nozzle comprising: an airfoil having: a suction side; a pressure side opposing the suction side; a leading edge spanning between the pressure side and the suction side; and a trailing edge opposing the leading edge and spanning between the pressure side and the suction side; and at least one endwall connected with the airfoil along the suction side, pressure side, trailing edge and the leading edge, wherein at least one of the pressure side or the suction side of the airfoil includes a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in TABLE I, wherein the coordinate values are non-dimensional values of from 0 to 1 convertible to distances by multiplying the values by a leading edge height expressed in units of distance, and wherein X and Y values connected by smooth continuing arcs define airfoil profile sections at each distance Z along the airfoil, the profile sections at the Z distances being joined smoothly with one another to form the airfoil profile, wherein the Cartesian coordinate values have an origin at a root of the leading edge of the airfoil.
 18. The turbine of claim 17, wherein the at least one endwall includes an axisymmetric contour.
 19. The turbine of claim 18, wherein the axisymmetric contour includes a thickened area having an apex at approximately 50% axial chord downstream of the leading edge.
 20. The turbine of claim 18, wherein the thickened area extends across at least approximately 10 percent of an axial length of the endwall, and extends across an entire pitch of the turbine nozzle. 